If a continuous random variable x has the probability density function ?->(Show Answer!)

1. If a continuous random variable x has the probability density function

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MCQ-> Analyze the following passage and provide appreciate answers for the questions that follow. Ideas involving the theory probability play a decisive part in modern physics. Yet we will still lack a satisfactory, consistence definition of probability; or, what amounts to much the same, we still lack a satisfactory axiomatic system for the calculus of probability. The relations between probability and experience are also still in need of clarification. In investigating this problem we shall discover what will at first seem an almost insuperable objection to my methodological views. For although probability statements play such a vitally important role in empirical science, they turn out to be in principle impervious to strict falsification. Yet this very stumbling block will become a touchstone upon which to test my theory, in order to find out what it is worth. Thus, we are confronted with two tasks. The first is to provide new foundations for the calculus of probability. This I shall try to do by developing the theory of probability as a frequency theory, along the lines followed by Richard von Mises, But without the use of what he calls the ‘axiom of convergence’ (or ‘limit axiom’) and with a somewhat weakened ‘axiom of randomness’ The second task is to elucidate the relations between probability and experience. This means solving what I call the problem of decidability statements. My hope is that the investigations will help to relieve the present unsatisfactory situation in which physicists make much use of probabilities without being able to say, consistently, what they mean by ‘probability’.The statement, “The relations between probability and experience are still in need of clarification” implies that:
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MCQ->If a continuous random variable x has the probability density function....

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MCQ-> The passage below is accompanied by a set of six questions. Choose the best answer to each question. During the frigid season... it's often necessary to nestle under a blanket to try to stay warm. The temperature difference between the blanket and the air outside is so palpable that we often have trouble leaving our warm refuge. Many plants and animals similarly hunker down, relying on snow cover for safety from winter's harsh conditions. The small area between the snowpack and the ground, called the subnivium... might be the most important ecosystem that you have never heard of.The subnivium is so well-insulated and stable that its temperature holds steady at around 32 degree Fahrenheit (0 degree Celsius). Although that might still sound cold, a constant temperature of 32 degree Fahrenheit can often be 30 to 40 degrees warmer than the air temperature during the peak of winter. Because of this large temperature difference, a wide variety of species...depend on the subnivium for winter protection.For many organisms living in temperate and Arctic regions, the difference between being under the snow or outside it is a matter of life and death. Consequently, disruptions to the subnivium brought about by climate change will affect everything from population dynamics to nutrient cycling through the ecosystem.The formation and stability of the subnivium requires more than a few flurries. Winter ecologists have suggested that eight inches of snow is necessary to develop a stable layer of insulation. Depth is not the only factor, however. More accurately, the stability of the subnivium depends on the interaction between snow depth and snow density. Imagine being under a stack of blankets that are all flattened and pressed together. When compressed, the blankets essentially form one compacted layer. In contrast, when they are lightly placed on top of one another, their insulative capacity increases because the air pockets between them trap heat. Greater depths of low-density snow are therefore better at insulating the ground.Both depth and density of snow are sensitive to temperature. Scientists are now beginning to explore how climate change will affect the subnivium, as well as the species that depend on it. At first glance, warmer winters seem beneficial for species that have difficulty surviving subzero temperatures; however, as with most ecological phenomena, the consequences are not so straightforward. Research has shown that the snow season (the period when snow is more likely than rain) has become shorter since l970. When rain falls on snow, it increases the density of the snow and reduces its insulative capacity. Therefore, even though winters are expected to become warmer overall from future climate change, the subnivium will tend to become colder and more variable with less protection from the above-ground temperatures.The effects of a colder subnivium are complex... For example, shrubs such as crowberry and alpine azalea that grow along the forest floor tend to block the wind and so retain higher depths of snow around them. This captured snow helps to keep soils insulated and in turn increases plant decomposition and nutrient release. In field experiments, researchers removed a portion. of the snow cover to investigate the importance of the subnivium's insulation. They found that soil frost in the snow-free area resulted in damage to plant roots and sometimes even the death of the plant.The purpose of this passage is to
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